Introduction The cross validation is a common technique to calibrate the binwidth histogram. They are the simplest and, sometimes, the most effective tool to describe the density of some dataset.

I will make a summary of ideas about nonparametric estimation, including some basics results to develop more advanced theory later. In the first post we talk something about the density estimation and the nonparametric regression. Later, in posts about histogram (I,II,III,IV) , we saw how the histogram is a nonparametric estimator and we studied its …

Today we will apply the ideas of the others post by a simple example. Before, we are going to answer the question of the last week. What is exactly the $latex {h_{opt}}&fg=000000$ if we assume that $latex \displaystyle \displaystyle f(x) = \frac{1}{\sqrt{2\pi}} \text{exp}\left(\frac{-x^2}{2}\right)? &fg=000000$ How $latex {f(x)}&fg=000000$ is the density of standard normal distribution. It is …

Before to continue with today’s post we will answer the question of last week, Is it $latex {\hat{f}_{h}(x)}&fg=000000$ a consistent estimator? The answer is yes. Because convergence in mean squared implies convergence in probability.

We continue our presentation about the estimation of histograms and its statistical properties. Today we will start the theory for reducing the mean squared error. In order to study the statistical properties of $latex {\hat{f}_{h}(x)}&fg=000000$We will start introducing the concept of mean squared error (MSE) or quadratic risk. We define

We are going to introduce the histogram as a simple nonparametric density estimator. I will divide this presentation in several posts for simplicity reasons. Let us $latex {X_1,\ldots,X_n}&fg=000000$ with pdf $latex {f}&fg=000000$. The histogram is the simplest nonparametric estimator of $latex {f}&fg=000000$.